function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%



%Part 1

% Add ones to the X data matrix
X = [ones(m, 1) X];
X_h = [ones(m, 1) sigmoid(X*Theta1')];
X_o = sigmoid(X_h*Theta2');
p = zeros(m, num_labels);
% 初始化对应的map出的Y
for i = 1:m
  p(i,y(i)) = 1;
end
% 所有误差值矩阵
B = p.*log(X_o) + (1-p).*log(1-X_o);
J = sum(B(:))*-1/m;
%计算正则项
t_1 = Theta1(:,2:end);
t_2 = Theta2(:,2:end);
t_1 = t_1.*t_1;
t_2 = t_2.*t_2;
regular = (sum(t_1(:))+sum(t_2(:)))*lambda/(2*m);
%输出最终的代价
J = J+regular; 

%Part 2

%反向传递
z_2 = [ones(m,1) X*Theta1']';
delta_3 = (X_o-p)';
delta_2 = (Theta2'*delta_3).* sigmoidGradient(z_2);%注意这里传入的是z不是a!
delta_2 = delta_2(2:end,:);
%最终求导
D_1 = zeros(size(delta_2,1),size(X,2));
D_2 = zeros(size(delta_3,1),size(X_h,2));
for t =1:m 
  D_1 = D_1 .+ delta_2(:,t)*X(t,:);
  D_2 = D_2 .+ delta_3(:,t)*X_h(t,:);
end
Theta1_grad = D_1/m;
Theta2_grad = D_2/m; 
%测试

%添加正则项
t_1 = Theta1(:,2:end);
t_2 = Theta2(:,2:end);
t_1 = [zeros(size(Theta1,1),1) t_1];
t_2 = [zeros(size(Theta2,1),1) t_2];
Theta1_grad = Theta1_grad+lambda*t_1/m;
Theta2_grad = Theta2_grad+lambda*t_2/m;











% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
